You do have the right to trim overhanging branches etc in any case, but this will not help if the majority of the issue is on the other side of the fence.
In the UK, you can contact your local authority and ak for the officer responsible for High Hedges. They usually work in the Planning or Environmental Health departments, and every authority in England and Wales will have a designated officer.
Two or three years back there was legislation introduced in England and Wales which empowered local authorities to act as mediators in High Hedge complaints, in response to an overwhelming number of issues arising from leylandii hedging/trees, which grow very high very quickly.
This is completely separate from ASBO legislation - it can be very difficult to prove that failure to maintain a hedge constitutes Anti Social Behaviour in some local authority areas.
The High Hedges officer will expect you to have made some effort to communicate your concenrs with your neighbour, an will act as mediator if no satisfactory solution can be concluded between yourselves. Once they act as mediators, it can sometimes go so far as the authority taking legal action to force your neighbour into remedial action.
I used to work in Local authority and now work for a software company which provides local authorities with solutions for statutory and legislative functions - I specialise in Planning, and provide consultancy on High hedges legislation and solutions.